The Rare Event Approach is a
way of thinking about the relationship between Rare

Events and Random Samples.
This approach will be useful to us later in the course.

Suppose we have an
experiment, which we use to generate random samples, and suppose further that
we have a particular event, denoted E, which might be rare. We will evaluate
the rarity of the event E using a random sample.

We can state the Rare Event Assumption (REA) as follows:

The probability of
observing event E is approximately 0.

If the REA holds true, then
it is not likely that any single random sample will exhibit the event E…

So, suppose that we have a
random sample, and suppose further that the sample exhibits the event E.

Then either the REA holds
true, and we have observed an exceptionally rare random sample; or the REA does
not hold, and it is not unusual for any single random sample to exhibit the
event E.